scholarly journals Uniform Stability Analysis of Fractional-Order BAM Neural Networks with Delays in the Leakage Terms

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Xujun Yang ◽  
Qiankun Song ◽  
Yurong Liu ◽  
Zhenjiang Zhao
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Equilibrium Point ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Uniform Stability ◽  
Bam Neural Networks ◽  
Analysis Method ◽  
Inequality Technique ◽  
Delay Dependent

A class of fractional-order BAM neural networks with delays in the leakage terms is considered. By using inequality technique and analysis method, several delay-dependent sufficient conditions are established to ensure the uniform stability of such networks. Moreover, the sufficient conditions guaranteeing the existence, uniqueness, and stability of the equilibrium point are also obtained. In addition, three simulation examples are given to demonstrate the effectiveness of the obtained results.

EXPONENTIAL STABILITY ANALYSIS OF NEURAL NETWORKS WITH VARIABLE DELAYS

2010 ◽  
Vol 20 (05) ◽  
pp. 1541-1549 ◽  
Author(s):  
MAN-CHUN TAN ◽  
YAN ZHANG ◽  
WEN-LI SU ◽  
YU-NONG ZHANG
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Variable Delays

Some sufficient conditions to ensure the existence, uniqueness and global exponential stability of the equilibrium point of cellular neural networks with variable delays are derived. These results extend and improve the existing ones in the literature. Two illustrative examples are given to demonstrate the effectiveness of our results.

scholarly journals Global Mittag–Leffler Stabilization of Fractional-Order BAM Neural Networks with Linear State Feedback Controllers

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Hongyun Yan ◽  
Yuanhua Qiao ◽  
Lijuan Duan ◽  
Ling Zhang
Keyword(s):  
Neural Networks ◽  
Lyapunov Function ◽  
Fractional Order ◽  
State Feedback ◽  
Control Strategies ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Bam Neural Networks ◽  
Linear State ◽  
The Stability

In this paper, the global Mittag–Leffler stabilization of fractional-order BAM neural networks is investigated. First, a new lemma is proposed by using basic inequality to broaden the selection of Lyapunov function. Second, linear state feedback control strategies are designed to induce the stability of fractional-order BAM neural networks. Third, based on constructed Lyapunov function, generalized Gronwall-like inequality, and control strategies, several sufficient conditions for the global Mittag–Leffler stabilization of fractional-order BAM neural networks are established. Finally, a numerical simulation is given to demonstrate the effectiveness of our theoretical results.

scholarly journals Existence and Exponential Stability of Equilibrium Point for Fuzzy BAM Neural Networks with Infinitely Distributed Delays and Impulses on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-17
Author(s):  
Yongkun Li ◽  
Lijie Sun ◽  
Li Yang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Time Scales ◽  
Sufficient Conditions ◽  
Distributed Delays ◽  
Bam Neural Networks ◽  
Stability Of Equilibrium ◽  
Fuzzy Bam Neural Networks ◽  
The Fixed Point Theorem

By using the fixed point theorem and constructing a Lyapunov functional, we establish some sufficient conditions on the existence, uniqueness, and exponential stability of equilibrium point for a class of fuzzy BAM neural networks with infinitely distributed delays and impulses on time scales. We also present a numerical example to show the feasibility of obtained results. Our example also shows that the described time and continuous neural time networks have the same dynamic behaviours for the stability.

STABILITY ANALYSIS OF IMPULSIVE COHEN-GROSSBERG NEURAL NETWORK WITH UNBOUNDED DISCRETE TIME-VARYING DELAYS

2007 ◽  
Vol 17 (05) ◽  
pp. 407-417 ◽  
Author(s):  
QIANKUN SONG ◽  
JINDE CAO
Keyword(s):  
Neural Network ◽  
Stability Analysis ◽  
Exponential Stability ◽  
Discrete Time ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Analysis Method ◽  
Inequality Technique ◽  
Stability Results

In this paper, the impulsive Cohen-Grossberg neural network with unbounded discrete time-varying delays is considered. By using the analysis method and inequality technique, several sufficient conditions are obtained to ensure the global exponential stability of the addressed neural network. These results generalize the existing relevant stability results. Two examples with simulations are given to show the effectiveness of the obtained results.

Delay‐dependent asymptotic stability of BAM neural networks with time delay

Kybernetes ◽  
2010 ◽  
Vol 39 (8) ◽  
pp. 1313-1321 ◽  
Author(s):  
Wu Xueli ◽  
Zhang Jianhua ◽  
Guan Xinping ◽  
Meng Hua
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Global Stability ◽  
Equilibrium Point ◽  
Sufficient Conditions ◽  
Welding Process ◽  
Double Layers ◽  
Bam Neural Networks ◽  
Unique Equilibrium ◽  
Content Type

PurposeThe purpose of this paper is to examine the criteria of uniqueness of the equilibrium point and the new stability criteria for stability of the equilibrium point. The new stability condition is dependent on the size of delays.Design/methodology/approachThe global asymptotic stability of a class of delayed bi‐directional associative memory (BAM) neural networks is studied. Some new sufficient conditions are presented for the unique equilibrium point and the global stability of BAM neural networks with time delays by constructing Lyapunov functions and using the linear matrix inequality. A numerical example is presented to illustrate the effectiveness of the theoretical results.FindingsBased on the mathematical method and matrixes inequality skill, some criteria are obtained which contain the unique equilibrium point and the global stability of BAM neural networks.Research limitations/implicationsThe paper proposes the new Lyapunov function and new skill to compose matrixes inequality.Practical implicationsA very useful method for BAM neural network to judge the uniqueness of the equilibrium point and stability.Originality/valueThe new mathematical model is proposed about the production process, and the new control method is used in the temperature system for a double layers welded pipe in welding process.

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